Macroeconomic Theory 2

Course Type: Graduate (1st Year Core)

Course Description: This course introduces theoretical and methodological underpinnings of modern macroeconomics

Mathematical Prerequisites: Calculus, Linear Algebra, Basic Probability Theory, Static and Dynamic Optimization

Programming Languages Used: Julia, Matlab (and Dynare), R

Note 1: A chapter by Fernandez-Villaverde, Rubio-Ramirez and Schorfheide covers many topics we will go through in this course. Click here

Note 2: Computer codes will be provided in class

Note 3: I do not check attendance. But, I give surprise quizzes in lieu of this

Note 4: No appointment, no meeting

Note 5: The materials covered in optional problem sets (click here) are examinable. They correspond to the self-study component of the course

Grades: Class Participation and Quizzes (20%), Midterm Exam (40%), Final Exam (40%)

Lecture Slides:

Theory:

0. A Review of Utility and Production Functions

1. Introduction to Modern Macroeconomics

1.1 Example with a CRRA Utility Function

1.2 Frisch Elasticity of Labor Supply

2. Real Business Cycle Models

2.1 Accuracy of Linear and Quadratic Approximations

3. New Keynesian Models

3.1 Short Notes on the Lucas Critique

3.2 Other Models of Price Rigidities

3.3 Information Rigidities

3.4 Solving Linear Rational Expectations Models Using Generalized Schur Decomposition

3.5 Solving the basic New Keynesian model in Matlab, Dynare, R, and Julia

4. Ricardian Equivalence

Methods:

5. Solving Stochastic Difference Equations

6. Linear Quadratic Dynamic Programming

6.1 Example with Permanent Income Model

7. Commitment vs. Discretion

7.1 Example with New Keynesian Model

7.2 Derivation of Quadratic Loss Function

8. Bayesian Estimation of DSGE Models

8.1 Short Notes on Generalized Method of Moments Estimation

8.2 Bayesian Estimation of Regression Models

8.3 Short Notes on the Kalman Filter and Smoother

9. Structural Vector Autoregressions

Topics:

10. Optimal Taxation

11. Consumption and Asset Prices

12. Small Open Economy New Keynesian Models

12.1 Dornbusch's Model of Exchange Rate

12.1.1 Analyzing Dornbusch's Model with a Phase Diagram

13. Financial Accelerator

13.1 Short Notes on the Modigliani-Miller Theorem

14. Medium Scale DSGE Model

Readings:

A. Lecture Notes and Manuals:

• Barillias, F., Bhandari, A., Colacito, R., Kitao, S., Matthes, C., Sargent, T. J., Shin, Y. “Practicing Dynare,” (http://www.tomsargent.com/research/AP_tom16.pdf)

• Bierens, H. J. “The Inverse of a Partitioned Matrix,” (http://www.math.chalmers.se/~rootzen/highdimensional/blockmatrixinverse.pdf)

• den Haan, W. “Dynare,” (http://www.wouterdenhaan.com/numerical/slidesdynare.pdf)

• Ellison, M. “Business Cycles and Macro Finance,” (http://users.ox.ac.uk/~exet2581/mphil/mphil.html)

• Ellison, M. “Techniques and Applications of Robust Control,” (http://users.ox.ac.uk/~exet2581/robust/robust.html)

• Griffoli, T. M. “DYNARE User Guide,” (http://www.dynare.org/documentation-and-support/user-guide/Dynare-UserGuide-WebBeta.pdf/view)

• Ho, T. “A Beginner's Course on Solving and Estimating DSGE Models,” (http://mx.nthu.edu.tw/~tkho/DSGE/dsge.html)

• Nimark, K. “Information, Learning and Expectations In Macro,” (http://www.kris-nimark.net/Info_2016.html)

• Sims, E. “Graduate Macro Theory II,” (https://www3.nd.edu/~esims1/grad_macro_17.html)

• Soderlind, P. “Monetary Policy,” (https://sites.google.com/site/paulsoderlindecon/home/courses/MonAll.pdf?attredirects=0&d=1)

• Stock, J. H. and Watson, M. W. “Recent Developments in Structural VAR Modeling,” (http://www.nber.org/WNE/slides7-14-08/Lecture7.pdf)

• Svensson, L. E. O. (2010). “Optimization under Commitment and Discretion, the Recursive Saddlepoint Method, and Targeting Rules and Instrument Rules: Lecture Notes,” (http://larseosvensson.se/files/papers/CommDiscTRIR.pdf)

B. Books and Journal Articles:

• Acemoglu, D. (2009). “Introduction to Modern Economic Growth,” Princeton Univeristy Press.

• Adda, J. and Cooper, R. W. (2003), “Dynamic Economics,” The MIT Books, The MIT Press.

• An, S. and Schorfheide, F. (2007). “Bayesian Analysis of DSGE Models,” Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.

• Anderson, G. S. (2008). “Solving Linear Rational Expectations Models: A Horse Race,” Computational Economics, vol. 31, pages 95-113.

• Anderson, G. S. and Moore, G. (1985). “A Linear Algebraic Procedure for Solving Linear Perfect Foresight Models,” Economics Letters, Elsevier, vol. 17(3), pages 247-252.

• Backus, D. K., Kehoe, P. J., and Kydland, F. E. (1993). “International Business Cycles: Theory vs. Evidence,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 14-29.

• Barro, R. J. (1974). “Are Government Bonds Net Wealth?,” Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec.

• Barro, R. J. and Gordon, D. B. (1983). “Rules, Discretion and Reputation in a Model of Monetary Policy,” Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.

• Barro, R. and Sala-i-Martin, X. (2003). “Economic Growth, 2nd Edition,” MIT Press Books, The MIT Press.

• Bencivenga, V. R. (1992). “An Econometric Study of Hours and Output Variation with Preference Shocks,” International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 449-71, May.

• Benigno, P. and Woodford, M. (2006). “Linear-Quadratic Approximation of Optimal Policy Problems,” NBER Working Papers 12672, National Bureau of Economic Research, Inc.

• Benveniste, L. M. and Scheinkman, J. A. (1979). “On the Differentiability of the Value Function in Dynamic Models of Economics,” Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.

• Bernanke, B. S. (1983). “Nonmonetary Effects of the Financial Crisis in Propagation of the Great Depression,” American Economic Review, American Economic Association, vol. 73(3), pages 257-76, June.

• Bernanke, B. S. and Gertler, M. L. (1989). “Agency Costs, Net Worth, and Business Fluctuations,” American Economic Review, American Economic Association, vol. 79(1), pages 14-31, March.

• Bernanke, B. S., Gertler, M., and Gilchrist, S. (1999). “The Financial Accelerator in a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, Taylor J. B. and Woodford, M. (ed.), edition 1, vol. 1, chapter 21, pages 1341-1393, Elsevier.

• Binder, M. and Pesaran, M. H. (1997). “Multivariate Linear Rational Expectations Models,” Econometric Theory, Cambridge University Press, vol. 13(06), pages 877-888, December.

• Blanchard, O. J. and Kahn, C. M. (1980). “The Solution of Linear Difference Models under Rational Expectations,” Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.

• Brainard, W. C. (1967). “Uncertainty and the Effectiveness of Policy,” American Economic Review Papers and Proceedings, pages 411-425.

• Braun, A. R. (1994). “Tax Disturbances and Real Economic Activity in the Postwar United States,” Journal of Monetary Economics, Elsevier, vol. 33(3), pages 441-462, June.

• Brock, W. A. and Mirman, L. J. (1973). “Optimal Economic Growth and Uncertainty: The No Discounting Case,” International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 560-73, October.

• Bullard, J. and Mitra, K. (2002). “Learning about Monetary Policy Rules,” Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.

• Cagan, P. (1956). “The Monetary Dynamics of Hyperinflation,” in Friedman, M. (ed.), Studies in the Quantity Theory of Money, University of Chicago Press.

• Calvo, G. A. (1983). “Staggered Prices in a Uility-maximizing Framework,” Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.

• Canova, F. (2007). “Methods for Applied Macroeconomic Research,” Princeton University Press.

• Cameron, A. C. and Trivedi, P. K. (2005). “Microeconometrics: Methods and Applications,” Cambridge University Press.

• Campbell, J. Y. (2000). “Asset Pricing at the Millennium,” Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, 08.

• Campbell, J. Y. and Cochrane, J. (1999). “Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,” Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.

• Chamley, C. (1986). “Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives,” Econometrica, Econometric Society, vol. 54(3), pages 607-22, May.

• Chow, G. (1997). “Dynamic Economics,” Oxford University Press.

• Christiano, L. J., Trabandt, M., and Walentin, K. (2010). “DSGE Models for Monetary Policy Analysis,” Handbook of Monetary Economics, in Friedman, B. M. and Woodford, M. (ed.), Handbook of Monetary Economics, edition 1, vol. 3, chapter 7, pages 285-367, Elsevier.

• Christiano, L. J., Eichenbaum, M., and Evans, C. L. (2005). “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.

• Clarida, R., Gali, J., and Gertler, M. (1999). “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.

• Clarida, R., Gali, J., and Gertler, M. (2001). “Optimal Monetary Policy in Open versus Closed Economies: An Integrated Approach,” American Economic Review, American Economic Association, vol. 91(2), pages 248-252, May.

• Collard, F. and Juillard, M. (2001). “A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model,” Computational Economics, Springer, vol. 17(2-3), pages 125-39, June.

• Cooley, T. F. and Prescott, E. C. (1995). “Economic Growth and Business Cycles,” Chapter 1 in T. F. Cooley (ed.), Frontiers of Business Cycle Research, Princeton University Press, pages 1–38.

• Debreu, G. (1954). “Valuation Equilibrium and Pareto Optimum,” Proceedings of the National Academy of Sciences, vol. 40(7), pages 588-592, July.

• DeJong, D. N. and Dave, C. (2011). “Structural Macroeconometrics,” Princeton University Press.

• Del Negro, M. and Schorfheide, F. (2008). “Forming Priors for DSGE Models (and How It Affects the Assessment of Nominal Rigidities),” Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1191-1208, October.

• den Haan, W. J. and Marcet, A. (1990). “Solving the Stochastic Growth Model by Parameterizing Expectations,” Journal of Business and Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.

• Diamond, P. A. (1982). “Aggregate Demand Management in Search Equilibrium,” The Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.

• Dixit, A. K. and Stiglitz, J. E. (1977). “Monopolistic Competition and Optimum Product Diversity,” American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.

• Dornbusch, R. (1976). “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-76, December.

• Epstein, L. G. and Zin, S. E. (1989). “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework,” Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.

• Fernández-Villaverde, J. and Rubio-Ramírez, J. F. (2006). “A Baseline DSGE Model,” Manuscript.

• Fernández-Villaverde, J. and Rubio-Ramírez, J. F. (2008). “How Structural Are Structural Parameters?,” NBER Chapters, in NBER Macroeconomics Annual 2007, vol. (22), pages 83-137, National Bureau of Economic Research, Inc.

• Fernández-Villaverde, J. (2009). “The Econometrics of DSGE Models,” NBER Working Papers 14677, National Bureau of Economic Research, Inc.

• Friedman, M. and Schwartz, A. J. (1963). “A Monetary History of the United States, 1867-1960,” NBER Books, National Bureau of Economic Research, Inc.

• Gali, J. (2008). “Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework,” Princeton University Press.

• Giannoni, M. P. and Woodford, M. (2003). “Optimal Interest-Rate Rules: II. Applications,” NBER Working Papers 9420, National Bureau of Economic Research, Inc.

• Gordon, R. J. (1990). “What Is New-Keynesian Economics?,” Journal of Economic Literature, American Economic Association, vol. 28(3), pages 1115-71, September.

• Gorman, W. M. (1953) “Community Preference Fields,” Econometrica, Econometric Society, vol. 21, pages 63–80.

• Guerrieri, L. and Iacoviello, M. (2015) “Occbin: A Toolkit to Solve Models with Occasionally Binding Constraints Easily,” Journal of Monetary Economics, Elsevier, vol. 70, pages 22-38, March.

• Hall, R. E. (1978). “Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence,” Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.

• Hamilton, J. D. (1994) “Time Series Analysis,” Princeton University Press.

• Hansen, G. D. (1985). “Indivisible Labor and the Business Cycle,” Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.

• Hansen, G. D. and Wright, R. (1994). “The Labor Market in Real Business Cycle Theory,” Chapter 18 in P.J. Miller (ed.), Rational Expectations Revolution, MIT Press Books, The MIT Press, 335-354.

• Hansen, L. P. (1982). “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.

• Hansen, L. P. and Sargent, T. J. (2008). “Robustness,” Princeton University Press.

• Hayashi, F. (1982). “Tobin's Marginal q and Average q: A Neoclassical Interpretation,” Econometrica, Econometric Society, vol. 50(1), pages 213-24, January.

• Herbst, E. P. and Schorfheide, F. (2016). “Bayesian Estimation of DSGE Models,” Princeton University Press.

• Hodrick, R. J. and Prescott, E. C. (1997). “Postwar U.S. Business Cycles: An Empirical Investigation,” Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.

• Hornstein, A. (1993). “Monopolistic Competition, Increasing Returns to Scale, and the Importance of Productivity Shocks,” Journal of Monetary Economics, Elsevier, vol. 31(3), pages 299-316, June.

• Iacoviello, M. (2005). “House Prices, Borrowing Constraints, and Monetary Policy in the Business cycle,” American Economic Review, American Economic Association, vol. 95(3), pages 739-764, June.

• Iacoviello, M. and Neri, S. (2010). “Housing Market Spillovers: Evidence from an Estimated DSGE Model,” American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 125-64, April.

• Judd, K. L. (1985). “Redistributive Taxation in a Simple Perfect Foresight Model,” Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.

• Judd, K. L. (1998). “Numerical Methods in Economics,” The MIT Books, The MIT Press.

• Kamihigashi, T. (2007). “Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks,” Journal of Mathematical Economics, vol. 43(3-4), pages 477-500.

• Kilian, L. (2013). “Structural Vector Autoregressions,” in Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 22, pages 515-554, Edward Elgar Publishing.

• Kim, I. and Loungani, P. (1992). “The Role of Energy in Real Business Cycle Models,” Journal of Monetary Economics, Elsevier, vol. 29(2), pages 173-189, April.

• King, R. G. and Plosser, C. I. (1984). “Money, Credit, and Prices in a Real Business Cycle,” American Economic Review, American Economic Association, vol. 74(3), pages 363-80, June.

• King, R. G. and Watson, M. W. (1998). “The Solution of Singular Linear Difference Systems under Rational Expectations,” International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.

• Kiyotaki, N. and Moore, J. (1997). “Credit Cycles,” Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 211-48, April.

• Klein, P. (2000). “Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423.

• Kydland, F. E. and Prescott, E. C. (1977). “Rules Rather than Discretion: The Inconsistency of Optimal Plans,” Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-91, June.

• Kydland, F. E. and Prescott, E. C. (1982). “Time to Build and Aggregate Fluctuations,” Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.

• Liu, P. (2006). “A Small New Keynesian Model of the New Zealand Economy,” Discussion Paper Series, Reserve Bank of New Zealand.

• Ljungqvist, L. and Sargent, T. J. (2004). “Recursive Macroeconomic Theory, 2nd Edition,” MIT Press Books, The MIT Press.

• Long, J. B. and Plosser, C. I. (1983). “Real Business Cycles,” Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.

• Lucas, R. E. (1972). “Expectations and the neutrality of money,” Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.

• Lucas, R. E. (1973). “Some International Evidence on Output-Inflation Tradeoffs,” American Economic Review, American Economic Association, vol. 63(3), pages 326-34, June.

• Lucas, R. E. (1975). “An Equilibrium Model of the Business Cycle,” Journal of Political Economy, University of Chicago Press, vol. 83(6), pages 1113-44, December.

• Lucas, R. E. (1978). “Asset Prices in an Exchange Economy,” Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.

• Lucas, R. E. (1987). “Models of Business Cycles,” Basil Blackwell.

• Lucas, R. E. and Sargent, T. J. (1979). “After Keynesian macroeconomics,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr.

• Mankiw, N. G. and Reis, R. (2002). “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1295-1328.

• Mankiw, N. G., Rotemberg, J. J., and Summers, L. H. (1985). “Intertemporal Substitution in Macroeconomics,” The Quarterly Journal of Economics, The MIT Press, vol. 100(1), pages 225-51, February.

• Manuelli, R. E. (1986). “Modern Business Cycle Analysis: A Guide to the Prescott-Summers Debate,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 3-8.

• McCall, J. J. (1970). “Economics of Information and Job Search,” The Quarterly Journal of Economics, Oxford University Press, vol. 84(1), pages 113-126.

• McGrattan, E. R. (1994). “The Macroeconomic Effects of Distortionary Taxation,” Journal of Monetary Economics, Elsevier, vol. 33(3), pages 573-601, June.

• Mehra, R. and Prescott, E. C. (1985). “The Equity Premium: A puzzle,” Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.

• Miao, J. (2014). “Economic Dynamics in Discrete Time,” The MIT Press Books, The MIT Press.

• Monacelli, T. (2005). “Monetary Policy in a Low Pass-Through Environment,” Journal of Money, Credit, and Banking, vol. 37(6), pages 1047-1066.

• Mortensen, D. T. (1982). “The Matching Process as a Noncooperative Bargaining Game,” In The Economics of Information and Uncertainty, University of Chicago Press, pages 233-258.

• Muth, J. F. (1960). “Optimal Properties of Exponentially Weighted Forecasts,” Journal of the American Statistical Association, vol. 55(290), pages 299-306.

• Obstfeld, M. and Rogoff, K. (1996). “Foundations of International Macroeconomics,” The MIT Press.

• Pesaran, M. H. and Smith, R. P. (2011). “Beyond the DSGE Straitjacket,” IZA Discussion Papers 5661, Institute for the Study of Labor (IZA).

• Pissarides, C. A. (1985). “Short-run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages,” American Economic Review, American Economic Association, vol. 75(4), pages 676-90, September.

• Pissarides, C. A. (1990). “Equilibrium Unemployment Theory,” The MIT press.

• Prescott, E. C. (1986). “Theory Ahead of Business Cycle Measurement,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 9-22.

• Ramey, V. A. (2016). “Macroeconomic Shocks and Their Propagation,” NBER Working Papers 21978, National Bureau of Economic Research, Inc.

• Rogerson, R. (1988). “Indivisible Labor, Lotteries and Equilibrium,” Journal of Monetary Economics, Elsevier, vol. 21(1), pages 3-16, January.

• Romer, D. (2012). “Advanced Macroeconomics, Fourth Edition,” McGraw-Hill Irwin.

• Sargent, T. J. (1987). “Dynamic Macroeconomic Theory,” Harvard University Press.

• Sargent, T. J. and Wallace, N. (1981). “Some Unpleasant Monetarist Arithmetic,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall.

• Schmitt-Grohe, S. and Uribe, M. (2004). “Solving Dynamic General Equilibrium Models Using a Second-order Approximation to the Policy Function,” Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.

• Shapiro, C. and Stiglitz, J. E. (1984). “Equilibrium Unemployment as a Worker Discipline Device,” American Economic Review, American Economic Association, vol. 75(4), pages 892-93, September.

• Sims, C. A. (2002). “Solving Linear Rational Expectations Models,” Computational Economics, Springer, vol. 20(1-2), pages 1-20, October.

• Smets, F. and Wouters, R. (2003). “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area,” Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.

• Smets, F. and Wouters, R. (2007). “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.

• Soderlind, P. (1999). “Solution and Estimation of RE Macromodels with Optimal Policy,” European Economic Review, Elsevier, vol. 43(4-6), pages 813-823, April.

• Stokey, N. L., Lucas, R. E., and Prescott, E. C. (1989). “Recursive Methods in Economic Dynamics,” Harvard Univeristy Press.

• Summers, L. H. (1986). “Some Skeptical Observations on Real Business Cycle Theory,” Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 23-27.

• Tobin, J. (1969). “A General Equilibrium Approach to Monetary Theory,” Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(1), pages 15-29, February.

• Townsend, R. M. (1979). “Optimal Contracts and Competitive Markets with Costly State Verification,” Journal of Economic Theory, Elsevier, vol. 21(2), pages 265-293, October.

• Uhlig, H. (1999), “A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily,” in Marimon, R. and Scott, A. (eds.), Computational Methods for the Study of Dynamic Economies, Oxford University Press.

• Villemot, S. (2011). “Solving Rational Expectations Models at First Order: What Dynare Does,” Dynare Working Papers 2, CEPREMAP.

• Walsh, C. E. (2010). “Monetary Theory and Policy, Third Edition,” MIT Press Books, The MIT Press.

• Woodford, M. (1999) “Commentary: How Should Monetary Policy Be Conducted in an Era of Price Stability?” in New Challenges for Monetary Policy: A Symposium Sponsored by the Federal Reserve Bank of Kansas City, Federal Reserve Bank of Kansas City, pages 277-316.

• Woodford, M. (2003). “Interest and Prices: Foundations of a Theory of Monetary Policy,” Princeton University Press.

• Yun, T. (1996). “Nominal Price Rigidity, Money Supply Endogeneity, and Business Cycles,” Journal of Monetary Economics, vol. 37(2-3), pages 345-370, February.